ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-18-8589-2018Subgrid-scale variability in clear-sky relative humidity and forcing by aerosol–radiation interactions in an atmosphere modelSubgrid-scale variability in clear-sky RH and forcing by aerosol–radiation interactionsPetersikPaulpaul.j.petersik@gmail.comSalzmannMarchttps://orcid.org/0000-0002-3987-2303KretzschmarJanhttps://orcid.org/0000-0002-8013-5831CherianRibuMewesDanielhttps://orcid.org/0000-0001-9959-1557QuaasJohanneshttps://orcid.org/0000-0001-7057-194XLeipzig Institute for Meteorology, Universität Leipzig, Leipzig, GermanyPaul Petersik (paul.j.petersik@gmail.com)19June20181812858985997September201713November201717May201819May2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://acp.copernicus.org/articles/18/8589/2018/acp-18-8589-2018.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/18/8589/2018/acp-18-8589-2018.pdf
Atmosphere models with resolutions of several tens of kilometres take
subgrid-scale variability in the total specific humidity qt into account
by using a uniform probability density function (PDF) to predict fractional
cloud cover. However, usually only mean relative humidity,
RH‾, or mean clear-sky relative humidity,
RH‾cls, is used to compute hygroscopic growth
of soluble aerosol particles. While previous studies based on limited-area
models and also a global model suggest that subgrid-scale variability in RH
should be taken into account for estimating radiative forcing due to aerosol–radiation
interactions (RFari), here we present the first
estimate of RFari using a global atmospheric model with a parameterization
for subgrid-scale variability in RH that is consistent with the assumptions
in the model. For this, we sample the subsaturated part of the uniform RH-PDF
from the cloud cover scheme for its application in the hygroscopic growth
parameterization in the ECHAM6-HAM2 atmosphere model. Due to the non-linear
dependence of the hygroscopic growth on RH, this causes an increase in
aerosol hygroscopic growth. Aerosol optical depth (AOD) increases by a global
mean of 0.009 (∼7.8% in comparison to the control run). Especially
over the tropics AOD is enhanced with a mean of about 0.013. Due to the
increase in AOD, net top of the atmosphere clear-sky solar radiation,
SWnet,cls, decreases by -0.22Wm-2
(∼-0.08%). Finally, the RFari changes from -0.15 to
-0.19Wm-2 by about 31 %. The reason for this very
disproportionate effect is that anthropogenic aerosols are disproportionally
hygroscopic.
Introduction
Aerosols have a significant impact on the climate system by interacting with
radiation and clouds. Solar and thermal radiation interact with aerosols by
absorption and scattering processes. Despite extensive research on
atmospheric aerosols, the effective radiative forcing due to
aerosol–radiation interactions (ERFari) has still a large uncertainty. The
ERFari combines effects from radiative forcing due to aerosol–radiation
interactions (RFari) and rapid adjustments and is estimated to be -0.45
(-0.95 to +0.05) Wm-2 by the 5th assessment report (AR5) of the
Intergovernmental Panel on Climate Change (IPCC; ). The
radiative forcing by aerosol–radiation interactions from sulfate
(-0.4 Wm-2) and nitrate (-0.11 Wm-2) is a cooling effect
on the radiative balance of the Earth due to increased scattering of solar
radiation. In contrast, black carbon (+0.4 Wm-2) is warming the
Earth's climate due to absorption of solar radiation. Additionally, it is
uncertain if primary and secondary organic aerosols, aerosols from biomass
burning and mineral dust have a net cooling or a warming effect
e.g.. In total, anthropogenic
aerosols have very likely a cooling effect through aerosol–radiation
interactions on the radiative balance of the Earth .
Through non-linear relationships described by the Beer–Lambert law
and Mie scattering
, the extinction of radiation is related to the
aerosol particle radius. The aerosol particle radius of hygroscopic aerosols
like sulfate or sea salt aerosols increases in a humid environment due to
attraction of water. This hygroscopic growth is a non-linear function of the
ambient relative humidity (RH), where hygroscopic growth is especially
enhanced close to saturation . Therefore,
extinction due to hygroscopic aerosols increases strongly when the humidity
of the ambient air approaches saturation
.
It is known that humidity varies on subgrid scales in general circulation
models (GCMs) with largest subgrid-scale variability in the middle
troposphere (e.g. ). However, GCMs that just use
the grid-box mean relative humidity RH‾ to calculate
hygroscopic growth of aerosols do not take this subgrid-scale variability in
humidity and its effect on radiation into account. Studies based on
limited-area models suggest that GCMs may underestimate the RFari of sulfate
aerosols by 30 to 80 % when not considering subgrid-scale variability in RH
for the hygroscopic growth of sulfate particles
.
These studies use high-resolution models and compare the results from
calculations of radiative forcing that keep the high resolution of RH with
either calculation where RH is averaged spatially beforehand to mimic a GCM
resolution or results from model configurations with a coarser resolution. In
addition, recent studies show that models with a coarse resolution which do
not take subgrid-scale variability in various aerosol properties into account
underestimate aerosol radiative forcing ,
and have a significant negative bias in aerosol optical depth (AOD; ).
First attempts to implement a subgrid-scale variability in RH in a GCM for
the calculation of RFari by sulfate were made by
and . However,
these studies make strong simplifications about the shape of the used
probability density function (PDF) and are not consistent with the cloud
cover scheme. prescribe the RH
distribution globally for clear skies. For each grid cell and height
level, five fixed RH values are taken from a normal distribution around
RH = 70 %. They find that RFari by sulfate is 24 % greater than the
non-hydrated forcing when using the grid-box mean RH. However, RFari by
sulfate increases up to 37 % when the subgrid-scale variability in RH is
applied and the correlation between clouds and areas of high relative
humidity is taken into account. Hence, RFari by sulfate increased by about
10 % from simulations that use grid-box mean RH to simulations with a
subgrid-scale variability in RH. have a more
sophisticated approach. They use a triangular-shaped relative humidity
distribution around the grid-box mean RH with a magnitude of ±10 % that
is truncated at RH = 1.0 as proposed by
. They show that RFari by sulfate is
enhanced by 9 % due to the subgrid-scale variability in RH when clouds are
included. We want to point out that do not
consider variations in width and shape of the used distribution. This is a
rather strong simplification (especially having the non-linear hygroscopic
growth in mind) in comparison to findings of
that suggest a change of the width of a uniform PDF from about ±20 % at
the surface to about ±65 % in the middle troposphere.
In this study, we implement a stochastic parameterization of subgrid-scale
variability of clear-sky relative humidity RHcls into the
global aerosol-climate model of the Max Planck Institute for Meteorology
(MPI-M) ECHAM6-HAM2 . For
this, we use a uniform PDF that reproduces the
subsaturated part of the cloud cover scheme from
that is used by ECHAM6
. The width of the PDF from the cloud cover
scheme is a function of height . Hence, our parameterization inherits this feature.
ECHAM6-HAM2 until now used the grid-box mean clear-sky relative humidity
RH‾cls to calculate hygroscopic growth
. Now, rather than using the grid-box mean, the PDF
of the subgrid-scale variability in RHcls is randomly sampled for
each time step, grid cell and height level to compute the growth factor
gf (see Sect. ). Hence, the parameterization
complies with the necessity to be consistent and to introduce as few as
possible empirical or tunable parameters. For a more elaborate discussion on the
topic in the literature, we refer to .
Furthermore, hygroscopic growth is computed in ECHAM6-HAM2 for all
hygroscopic aerosol constituents that are incorporated in the model.
Therefore, the effect of subgrid-scale variability in RHcls on
hygroscopic growth is included for all hygroscopic aerosol particles in the
model.
A very similar method of subgrid-scale variability in humidity is, for
example, applied on the convective scheme of the European Centre for Medium-Range
Weather Forecasts (ECMWF) ensemble prediction system by
. They show that their new stochastic
convective scheme generally improves the skill of the operational system for
most variables in the short to medium range in the mid-latitudes. More
generally, we want to emphasize that stochastic parameterizations are not
only a method to estimate uncertainties but also lead to a better representation
of the mean state of the atmosphere. This was recently summarized in
.
In Sect. of this article we describe the aerosol module HAM2
in more detail and introduce our stochastic parameterization of clear-sky
relative humidity. Then, in Sect. we investigate how the new
parameterization changes optical and radiative properties of the atmosphere.
Afterwards, the results are discussed in Sect. . Finally,
this study is summarized with an outlook for further research in
Sect. .
MethodsAerosol module HAM2
In this section, we briefly describe the aspects of the micro-physical
aerosol module HAM2 that are relevant for this
study. The micro-physical aerosol module HAM2 is the successor of its first
version that was introduced by . HAM2 is
built as an extension of the atmospheric GCM ECHAM6
. It incorporates the following aerosol
components: sulfate (SO4), black carbon (BC), organic carbon (OC), sea salt
(SS) and mineral dust (DU). The module predicts the evolution of the aerosol
population based on 7 log-normal modes (4 soluble, S, and 3 insoluble, I)
that describe the size distribution of atmospheric aerosols. The modes are
divided into Nucleation (N, r<0.005µm), Aitken (K, 0.005<r<0.05µm), Accumulation (A, 0.05<r<0.5µm) and Coarse
(C, r>0.5µm) and are abbreviated in the following such as
CS for soluble Coarse mode. The main soluble aerosol constituents are SS, SO4
and OC. DU and BC are considered as insoluble on emission. However, insoluble
aerosols can become soluble if they merge with soluble particles due to
internal mixing by ageing processes such as condensation and coagulation
.
Aerosol radiative properties are calculated for 24 spectral bands for
shortwave and 16 bands for longwave radiation using Mie theory by applying
the algorithm suggested by . The model uses the
volume-weighted average refractive indices for internally mixed aerosols
where aerosol water is included . The effective complex radiative indices and the
Mie size parameter are then used for the aerosol radiative properties, namely
extinction cross section, single scattering albedo and asymmetry parameter
in the radiation scheme. For version 2 of the aerosol module, the
refractive indices for black carbon were updated with values from
that led to a reduction of the negative bias due to
aerosol absorption enhancement . In contrast to
and , HAM2 does
not include a very strong absorption enhancement for absorbing particles
inside clouds. It should be noted that the hypothesis of
is very controversial and not supported
by most other studies
e.g..
Hygroscopic growth in HAM2
Soluble particles can grow in size due to the attraction of water. This
hygroscopic growth can be described by the growth factor
gf=rwet/rdry, where rwet and
rdry are the wet and dry radius of an aerosol particle,
respectively. introduced the κ-Köhler
theory to calculate the growth factor as a function of relative humidity and
temperature
RHexpAK(T)Ddrygf=gf3-1gf3-(1-κ),
where RH is the ambient relative humidity, Ddry the dry diameter,
AK the temperature-dependent parameter of the Kelvin (curvature)
effect and κ the hygroscopicity. A κ value of 0 describes
completely hydrophobic aerosols, whereas κ values greater than 0.5
describe very hygroscopic aerosols. Aerosol constituents with very high
κ values in HAM2 are sulfate and sea salt (see Table ). Note that the κ value for sulfate in HAM2 is in the
range of the observed value for ammonium sulfate (0.33–0.72; ). Furthermore, HAM2 does not include nitrate in
its current set-up. The hygroscopicity of internally mixed aerosols is
determined by calculating the volume-weighted average of the κ values
form each soluble compound. In Eq. () gf is a
strictly monotonically increasing, non-linear function with positive
curvature for RH∈[0,1].
κ values as used in HAM2 from . The
κ value for sulfate in HAM2 is in the range of the observed value for
Ammonium sulfate . Furthermore, HAM2 does not
include nitrate in its current set-up.
ECHAM6-HAM2 uses the grid-box mean clear-sky relative humidity
RH‾cls in Eq. () to calculate
the hygroscopic growth for each aerosol mode.
RH‾cls is chosen, instead of grid-box mean
relative humidity RH‾, because
RH‾cls is a better estimate for the relative
humidity in the cloud-free part of a grid cell than RH‾
and cloud processing and cloud radiative effects are dominant in the cloudy
part of a grid box as reasoned in for
ECHAM5-HAM1. This means that since the aerosol–radiation interactions have a
small effect compared to the cloud reflectivity in the cloudy part of a grid
cell, swelling is only approximately treated in the cloudy part.
RH‾cls is diagnosed from predicted
RH‾. For this, saturation is assumed in clouds
(RH=1). When the grid box is cloud free (f=0) or partly cloudy
(0<f<1), clear-sky relative humidity is computed by
RH‾cls=RH‾-f/(1-f), where f is the fractional cloud cover. For overcast
grid boxes (f=1), the clear-sky relative humidity is set to saturation as
well (RH‾cls=1). Using the
RH‾cls in Eq. () implies that no
subgrid-scale variability in RHcls is used beyond the
information supplied by the fractional cloud cover.
(a) Scheme for predicting fractional cloud cover, f, with a
uniform PDF for the total-water qt. The blue area indicates the
fraction of a grid cell which is covered by clouds. ΔRHcls is set to Δq/qs=1-RHcrit for a PDF around
RH‾cls if no fractional cloud cover is present
(not depicted) or set to (qs-qcls)/qs=1-RH‾cls if fractional cloud cover is present
(in the figure shown in terms of specific humidity). (b) Cumulative
distribution function (CDF) for a uniform PDF around
RH‾cls. By the inversion of the CDF and with a
random number a∈[0,1] (see Eq. ), a value between
RHcls-ΔRHcls and
RHcls+ΔRHcls is sampled and used as
the argument for the hygroscopic growth.
Stochastic parameterization for the subgrid-scale variability in clear-sky relative humidity
In the ECHAM model, subgrid-scale variability in specific humidity is already
used for the prediction of fractional cloud cover
. The cloud scheme assumes a uniform
PDF as proposed by
for the horizontal subgrid-scale
variability of total-water qt between q¯t-Δq
and q¯t+Δq, where Δq=γqs
(see Fig. a). Variable q¯t is the model-predicted
grid-box mean total-water specific humidity and qs the saturation
specific humidity computed from the predicted grid-box mean temperature. The
scaling parameter γ is varying in the vertical but otherwise assumed
to be constant in space and time. It can be calculated by γ=1-RHcrit, where RHcrit is the critical
relative humidity that is a function of height
. Fractional cloud cover
occurs if the grid-box mean relative humidity RH‾
exceeds the critical relative humidity. In ECHAM6-HAM2,
RHcrit is parameterized by
RHcrit(p)=ct+(cs-ct)exp1-pspnx,
with p the ambient pressure and ps the surface pressure.
Furthermore, ct=0.7 and cs=0.9 are the critical
relative humidity values at the top of the atmosphere (TOA) and the surface,
respectively, and nx=4. The given values for ct,
cs and nx are the same as in the in the cloud cover scheme of
ECHAM6 in the standard set-up. Note that satellite observations analysed by
suggest a considerably stronger vertical change
with ct=0.34 in less stable regions and ct=0.37.
However,
we keep the values for ct, cs and nx as in the
standard set-up to ensure the comparability with older studies. While the
formulation of RHcrit is specific to the ECHAM6 model, the
cloud cover scheme from has also been
applied in other global models. Furthermore, the cloud cover
scheme which is, for example, used in the Geophysical Fluid Dynamics Laboratory
(GFDL) atmosphere model AM3 assumes a uniform PDF of total
water as well.
Several global atmosphere models including ECHAM6-HAM2 already make
assumptions to account for the subgrid-scale variability in other atmospheric
variables, e.g. for vertical velocity when computing droplet activation rates
. However, subgrid-scale variability in RH or
RHcls is not taken into account when computing hygroscopic
growth of interstitial aerosols except in some studies that made strong
simplifications regarding the shape and variation in the used PDF as explained
in the introduction
.
For our stochastic parameterization of subgrid-scale variability in
RHcls, we use the subsaturated part of the qt-PDF from the
cloud cover scheme in not-overcast cases (see Fig. a). This
diagnosed PDF is transformed into a RHcls-PDF dividing it by
qs. Afterwards, it is sampled for the stochastic parameterization of
subgrid-scale variability in RHcls. The width of the
qt-PDF in the cloud cover scheme is
2Δq=2γqs=2⋅(1-RHcrit)qs.
Dividing Eq. () by qs yields the width of the corresponding
RH-PDF. For cloud-free grid boxes this RH-PDF is equivalent to the
RHcls-PDF. In this case, its width is
2ΔRHcls=2Δqqs=2⋅(1-RHcrit).RHcrit is computed by Eq. ().
However, when fractional cloud cover is present ΔRHcls has to be adjusted to
ΔRHcls=qs-qclsqs=1-RH‾cls
so that the variation in RHcls occurs in the subsaturated part of the cloud cover PDF (see Fig. a).
Afterwards, instead of using RH‾cls as input
for the calculation of the gf, a stochastic value for clear-sky
relative humidity, RHcls,new, from the inversion of the
cumulative distribution function (CDF) is drawn (see
Fig. b). For this, a random number, a∈[0,1], is
generated and inserted into the following equation:
RHcls,new=RH‾cls+ΔRHcls(2a-1).
Note that the integration of the model is not fully deterministic in the current setting. If one preferred a deterministic model, one could configure the random
number generator such that in each integration the same random numbers are
generated.
Model settings and postprocessing
ECHAM-HAM2 is run with a resolution of T63L31. For aerosol emissions, the
AEROCOM II data for 1850 for pre-industrial (PI) and for 2000 for present-day
(PD) simulations are used (; see
Data availability). Climatological sea surface temperature (SST) and sea ice
distributions are prescribed. Ten-year free-running (no nudging)
model simulations starting on 1 January 2000 are performed with PI and PD aerosol
emissions, both with and without the new parameterization. The total effective radiative forcing (ERF) by
anthropogenic aerosols, ERFaer, is computed by
ERFaer=(SWnet+LWnet)PD-(SWnet+LWnet)PI,
where the short and longwave radiative fluxes, SW and LW, are at the TOA. The radiative forcing due to aerosol–radiation
interactions, RFari, is computed as suggested by :
RFari=(SWnet-SWnet,clean)PD-(SWnet-SWnet,clean)PI.
Again, radiative fluxes are at TOA. The subscript “clean” indicates the results of the radiative transfer equation for an atmosphere with no aerosols.
To depict changes in hygroscopic growth we define the squared ratio
β=gfstochgfcontrol2,
where gfstoch and gfcontrol account
for the growth factor in the model run with the stochastic parameterization
and the control model run, respectively. The squared ratio scales with the
effective extinction cross section and therefore describes the influence on
AOD.
Satellite retrievals of AOD from the Moderate Resolution Imaging
Spectroradiometer (MODIS) platform Aqua from the
period between August 2002 and December 2010 are used to evaluate the results
of implementing subgrid-scale variability in RHcls into
the model. The temporal mean values of AOD measurements
(AOD‾MODIS) for the entire time span
(August 2002–December 2010) are compared to the temporal means (January 2000–December 2009) of
the model data (AOD‾control,
AOD‾stoch).
(a) Profile of the global mean of the squared ratio of the growth
factor between the run with the stochastic parameterization of hygroscopic
growth, gfstoch, and the control run,
gfcontrol. CS is the soluble Coarse aerosol mode (red).
AS the soluble Accumulation (green), KS the soluble Aitken (blue) and NS the
soluble Nucleation aerosol mode (black). (b) Profile of global mean clear-sky
relative humidity (dark blue line) with its corresponding range of
subgrid-scale variability (light blue area).
Results
In the following, results from PD simulations, if not specified differently,
are presented. We compute uncertainties for a 95 % confidence interval on
the basis of yearly mean values from the temporal variability. In these differences,
uncertainties are added in quadrature.
In Fig. a the global mean profiles of β are shown for all
soluble aerosol modes. Hygroscopic growth of aerosols is in general enhanced
due to the implementation of a subgrid-scale variability in
RHcls. We find that the effect is stronger for aerosol
particles with a large particle radius. Thus, the effect is strongest for
particles from the CS mode (red line in Fig. a) and weakest for
particles from the NS mode (black line in Fig. a). Moreover,
the effect on hygroscopic growth has a maximum between 700 and
600 hPa
for each aerosol mode.
The global mean AOD increases by 0.009±0.002 (∼ 7.8 %). The
response in AOD is weaker in simulations with PI emissions with a global mean
difference of 0.006±0.002 (∼6.0 %). Figure a shows
that the AOD increased especially in lower latitudes with a mean of about
0.013 in the tropics. Furthermore, the figure reveals that the AOD of
diagnosed aerosol water (WAT) dominates the change in total AOD and not the
change in dry matter of SS or SO4. Figure b shows the zonal mean
AOD values from the model runs with and without the stochastic
parameterization and from satellite measurements of MODIS-Aqua. Changes due
to the new parameterization are small in comparison to the general difference
between modelled and measured AOD. The absorption aerosol optical depth
(AAOD) increased by 0.12±0.04×10-3 (∼4.7 %), mainly due
to an increase in AAOD by BC of about 0.11×10-3. However, note
that in absolute terms the change in AOD is nearly 2 orders of magnitude
greater than the change in AAOD.
Furthermore, the implementation of the new parameterization enhanced the
ratio of scattering efficiency to total extinction efficiency, ω, for
the CS, AS and KS aerosol modes with a maximum for the KS mode (2.6 %).
The effective extinction cross section, σ, increases for the CS, AS
and KS aerosol modes as well. The strongest change is visible for the KS mode
with a change by 15.1 %. Note that no output for ω and σ is
generated by the model for NS mode. Finally, the Ångström exponent for
wet particles, α, changes by -0.8 × 10-3±11.5×10-3 (-0.11 %). The total cloud cover decreased by -0.08±0.14 %
in PD simulations. In contrast, it increased by 0.17±0.14 in PI
simulations. The global mean profile of cloud cover f in Fig.
reveals a slight increase in cloud cover between 700 and
900 hPa for PD simulations, whereas it mainly decreased below and above this
layer. However, in PI runs f increased for most parts of the atmosphere
with a very little decrease at around 600 hPa.
In the following, solar and thermal clear-sky radiation represent the
idealized solar and thermal irradiance that would arise from an atmosphere
if clouds were absent, whereas all-sky stands for the irradiance that takes
the effect of clouds into account. The net clear-sky solar radiation
SWnet,cls decreases by -0.22±0.07Wm-2. In addition,
the net all-sky solar radiation SWnet changes by
-0.34±0.22Wm-2. For PI emissions, the effect on
SWnet,cls is with a change of -0.13±0.06Wm-2, as
expected, smaller than for PD emissions. In contrast, a stronger effect in PI
runs than in PD runs is visible for SWnet (-0.47±0.19Wm-2). Responses in the thermal radiation (positive downward)
are small. The clear-sky thermal radiation LWnet,cls has a slight
positive tendency with a mean value of 0.04±0.09Wm-2. Similar
to solar radiation, the all-sky thermal radiation LWnet changes
more than the clear-sky radiation with a global mean of 0.06±0.14Wm-2.
The comparison of 10-year model runs with PD and PI aerosol emissions
reveals a change of the RFari from -0.15±0.04 to
-0.19±0.04Wm-2 (31 %) in runs without and runs with the new
parameterization, respectively. This implies that subgrid-scale variability
of RHcls enhances the cooling effect of anthropogenic
aerosol emissions by aerosol–radiation interactions in climate simulations.
It is interesting to note that the RFari increases substantially given the
relatively small impact of the revision on present-day TOA balance. This can
be attributed to the fact that anthropogenic aerosol is disproportionally
hygroscopic. Furthermore, the effect on RFari translates into the ERF of
anthropogenic aerosols (ERFaer) that also has a negative tendency (-0.07±0.27). A summary of the influence of subgrid-scale variability in
RHcls on optical and radiative variables is given in
Table .
Changes in global mean values of optical and radiative variables due
to the implementation of subgrid-scale variability in
RHcls are listed. Uncertainties in the mean value are
calculated for a 95 % confidence interval on the basis of yearly mean values
from the temporal variability. Uncertainties in differences are added in
quadrature. Symbol ω is the ratio of the scattering efficiency to the total
extinction efficiency and σ the effective extinction cross section.
The indices KS, AS and CS indicate Aitken,
Accumulation and Coarse modes, respectively. Symbol α is the wet Ångström exponent,
SWnet the net shortwave radiation and with index
SWnet,cls the net shortwave radiation in the clear-sky part.
With the same meaning for the indices LW is the longwave radiation. TCC
is the total cloud cover. Results are presented for present-day and
pre-industrial emissions.
(a) Difference in temporally and zonally averaged AOD between the stochastic variation and the
control run in AOD for different aerosol constituents. AOD from diagnosed
aerosol water (WAT, blue) dominates the changes. (b) Temporally and zonally
averaged AOD from the control (solid) and stochastic (dashed) model
runs (black, January 2000–December 2009), and Moderate Resolution Imaging
Spectroradiometer Aqua satellite data (red,
August 2002–December 2010) is shown. Two discrepancies arise, namely (i) the fact
that the model diagnoses clear-sky AOD also in overcast grid cells, with a
relative humidity of RH = 1 in these cases, which are dismissed in the MODIS
retrieval and (ii) the point that MODIS uses a conservative cloud masking,
i.e. excludes pixels near cloud edges, whereas the model uses all clear-sky
pixels.
Discussion
As for the previous section, we discuss in the following the results from PD
simulations, if not specified differently. In model runs with the new
parameterization, aerosol particles swell stronger at each height level due to
the non-linear nature of hygroscopic growth (see Eq. ). The
positive curvature of this function for RHcls∈[0,1]
implies that by applying a uniform PDF on RHcls the
expected value of gf(RHcls) is greater than
gf(RH‾cls) with
RH‾cls being the grid-box mean clear-sky
relative humidity.
(a) Difference in cloud cover, f, due to the implementation of
subgrid-scale variability in RHcls for PI (dashed) and PD (solid)
simulations. (b) Global mean profile of mass mixing ratio for various aerosol
compounds from the CS mode.
Effects are stronger for aerosol particles with a larger radius, and thus
particles from CS and AS modes. Three reasons can explain the vertical shape
of the gf profiles:
Clear-sky relative humidity has a decreasing trend with height in the
model (see Fig. b). The same change in ΔRHcls in a drier environment leads to a smaller change in
gf in a more humid environment (unless saturation is reached)
because of the non-linearity of Eq. (). The effect of the
subgrid-scale variability in RHcls on gf is
therefore stronger in a more humid environment.
Very hygroscopic aerosol particles are more sensitive to changes in
relative humidity and larger particles tend to become deposited by impaction
and sedimentation more easily. The main hygroscopic aerosol types are
sulfate and sea salt, where sea salt (κ=1.12) is more hygroscopic
than sulfate (κ=0.6). Sea-salt particles are emitted at the surface
of the ocean. Due to their high κ value, sea-salt particles grow
strongly, are deposited easily and can not reach high altitudes. This is
indicated in Fig. b which shows that the mixing ratio of sea
salt decreases noticeably stronger with height than other aerosol compounds.
Hence, the aerosol composition of the atmosphere shifts towards less
hygroscopic components (smaller κ values) with height and the effect
of perturbing relative humidity on hygroscopic growth becomes weaker with
smaller κ values. This is supported by the study of
that examines the global distribution of κ
using the ECHAM/MESSy Atmospheric Chemistry (EMAC) model. They find that
especially at marine sites κ values decrease with height, whereas at
continental sites κ tends to be more constant with height.
Reasons 1 and 2 can only explain a decreasing trend of β with height but
not the maxima of the β profiles between 600 and 700 hPa.
The critical relative humidity determines the width of the PDF which is
used to vary RHcls stochastically. The width 2ΔRHcls of the PDF is calculated by ΔRHcls=1-RHcrit as described in
Sect. . But RHcrit is a function of height
(see Eq. ). It decreases from the surface to 600 hPa from 0.9
to close to 0.7. For higher altitudes, it is nearly constant and converges
slowly towards 0.7 (see Fig. b). This in fact means that the
width of the PDF increases with height from the surface to 600 hPa. Then, it
is almost constant. The positive curvature of Eq. () implies
that the wider the PDF is the stronger the mean hygroscopic growth. The
increasing width of the PDF explains why β becomes greater with height
until 600 hPa. Above, effects 1 and 2 are dominant and β decreases
again.
The AOD, the effective extinction cross section, σ, and the ratio of
scattering efficiency to total extinction efficiency, ω, are enhanced
because of the increase in the geometrical radius of the particles.
Anthropogenic aerosols that arise in PD simulations are disproportionally
hygroscopic. Therefore, hygroscopic aerosols swell stronger due to the new
parameterization in PD than in PI simulations and scatter more solar
radiation. This leads in turn to a higher AOD in PD than PI runs. The effect
of the new parameterization is especially strong for lower latitudes because
of the higher abundance of sea salt (not depicted) in these regions. In
addition, anthropogenic emissions of sulfate are strong in China, India and
over the Arabian Peninsula and contribute to the peak of increased AOD in the
northern tropics. Note that ECHAM6-HAM2 currently does not simulate nitrate
aerosols. The integration of nitrate aerosols will introduce very hygroscopic
aerosols into the model that would alter our results. As Fig. b
demonstrates, little can be said about improved skill of ECHAM-HAM2 to model
AOD in respect to AOD satellite retrievals of MODIS-Aqua.
The net clear-sky solar radiation SWnet,cls decreases (ΔSWnet,cls=-0.22Wm-2) due to an increased reflection of
solar radiation as indicated by an increased ω. However, the effect on
the net all-sky solar radiation SWnet is greater (ΔSWnet=-0.34Wm-2) than the effect on the net clear-sky
solar radiation. This is maybe due to the fact that although total cloud
cover (TCC) decreased by -0.08 %, cloud cover is slightly enhanced in
height levels between about 700 and 900 hPa (see graph for PD in Fig. ).
Hence, more solar radiation is reflected back to space by
these clouds.
We proceed with the discussion of differences that arise between PD and PI
simulations. The change in SWnet,cls is stronger for PD than for
PI emissions because backscattering of solar radiation is more enhanced by
the new parameterization in PD than in PI simulations because anthropogenic
aerosols are disproportionally hygroscopic. In addition, the response of
RFari (-0.04Wm-2, 31 %) indicates as well that the
parameterization leads to stronger backscattering by aerosols. Unexpectedly,
the response in SWnet is greater in PI runs (ΔSWnet,PI=-0.47Wm-2) than in PD runs (ΔSWnet,PD=-0.34Wm-2). We assume that this might be due
to the enhanced total cloud cover in the PI simulations (ΔTCCPI=0.17), whereas total cloud cover decreased in PD
simulations (ΔTCCPD=-0.08). We ascribe the differences in
cloud cover to internal variability. Hence, we suspect that the converse
results for SWnet arise due to internal variability. The stronger
increase in cloud cover for the higher troposphere in PI simulations (see
Fig. ) might explain the strong response of LWnet in
PI simulations (ΔLWnet,PI=0.26Wm-2). High, thin
clouds, namely cirrus clouds, are known to have a positive effect on outgoing
longwave radiation .
Conclusions
This study proposes a stochastic parameterization of clear-sky relative
humidity that is consistent with the cloud cover scheme for its application
in the aerosol hygroscopic growth parameterization. We investigate its effect
on hygroscopic growth of aerosol particles as well as the subsequent changes
in optical properties of the atmosphere and the radiative balance of the
Earth. The implementation of the new parameterization leads to stronger
swelling of aerosol particles (as expected) and therefore increases the AOD
(∼ 7.8 %). Furthermore, the increased AOD causes stronger
backscattering of solar radiation under clear-sky conditions
SWnet,cls (-0.08 %). Most importantly, the revision has a
very strong influence on the simulated radiative forcing due to
aerosol–radiation interaction RFari (31 %). In earlier studies RFari by
sulfate increased in GCMs by about 10 % when an idealized distribution for
RH was implemented .
Further studies found that GCMs underestimate RFari of sulfate when
subgrid-scale variability in RH is not taken into account by 73 % in a
limited-area model case study , by 30
to 80 % in a study that used a cloud-resolving model over a tropical ocean
and a mid-latitude continental region and by 30 to
40 % in a regional study (Europe and much of the North Atlantic) with a
high-resolution model . Hence, our study is in line
with previous studies based on limited-area models. The effect of including
RH subgrid variability, however, is bigger than the one found in the early
global model study by .
One might be able to further improve the parameterization of subgrid-scale
variability in RHcls by applying the subsaturated part of
the β-function from the optional cloud
cover scheme that prognostically treats the total-water variability PDF.
Furthermore, Fig. 2 in indicates that the
critical relative humidity, RHcrit, that defines the width of the
introduced RHcls-PDF varies horizontally on the same scale as
vertically. Therefore, the width of the RHcls-PDF could be
extended from just height-dependent to height- and zonal- or even height-,
zonal- and meridional-dependent.
The code for the subgrid-scale variability in RHcls is available upon request from the first
author.
The ECHAM6-HAM2 model output data used in this study is archived at the
Leipzig Institute for Meteorology (LIM) and at the German Climate Computing Center (DKRZ).
Data is available upon request from the
authors. Satellite data from MODIS-Aqua can be obtained at
https://neo.sci.gsfc.nasa.gov/, last access: 28 November 2014. AEROCOM emission data can be downloaded at
http://aerocom.met.no/emissions.html, last access: 4 May 2012.
The authors declare that they have no conflict of
interest.
Acknowledgements
The ECHAM-HAM model is developed by a consortium composed of ETH Zurich, Max
Planck Institut für Meteorologie, Forschungszentrum Jülich, University of
Oxford, the Finnish Meteorological Institute and the Leibniz Institute for
Tropospheric Research, and managed by the Center for Climate Systems Modeling
(C2SM) at ETH Zurich. The MODIS data are from the NASA Goddard Space Flight
Center. Funding by the European Research Council in
Starting Grant, grant agreement FP7-306284 (QUAERERE) is acknowledged.
We thank Steven J. Ghan and one anonymous reviewer for their work reviewing our
manuscript.
Edited by: Kostas Tsigaridis
Reviewed by: Steven J. Ghan and one anonymous referee
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